2.5 years required for an investment of 5000 dollars to grow to 6000 dollars at an interest rate of 7.5 percent per year, compounded quarterly.
Step-by-step explanation:
The given is,
Initial investment - $5000
Future amount - $6000
Interest rate - 7.5% (compounded quarterly)
Step:1
Formula to calculate the Future amount with compound interest,
...................................(1)
Where, F - Future amount
P - Initial amount
r - Rate of interest
n - No. of compounding in a year
t - Time period
From given,
F = $6000
P = $5000
r = 7.5%
n = 4 (compounded quarterly)
Equation (1) becomes,
Take log on both sides,
Substitute log values,
0.07918 = 4(t) (0.0080676)
= (t) (0.0322705)
= 2.45
t ≅ 2.5 years
Result:
2.5 years required for an investment of 5000 dollars to grow to 6000 dollars at an interest rate of 7.5 percent per year, compounded quarterly.
Answer:
Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:
Where 
and 
And for this case we select a sample size of n= 81. Since the distribution for X is normal then we know that the distribution for the sample mean 
is given by:
And the standard error of the mean would be:
4.1.5
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:
Where and
And for this case we select a sample size of n= 81. Since the distribution for X is normal then we know that the distribution for the sample mean is given by:
And the standard error of the mean would be:
4.1.5
Multiply the sales by the commission rate and add that to the base salary.
45,000 x 0.04 = 1,800
Total pay = 1800 + 380 = $2,180
-3x + 9 - 4 = x + 3 + 2x
-3x + 9 - 4 = 3x + 3
9 - 4 = 6x + 3
5 = 6x + 3
2 = 6x
1/3 = x
It is best to use mental math with some equations (5x5 or something that is easy enough that work does not have to be shown 10 dived by 5
